Satellite positioning systems use several satellites transmitting their positioning by radiofrequency signals to a receiver placed in the position to be located estimating the distances, called pseudo-distances, that separate it from the satellites based on the propagation time of the captured satellite signals. The receiver is located by a technique similar to triangulation and this location is all the more accurate when the positions of the satellites are known accurately to the receiver and the measurements of the pseudo-distances done by the receiver are accurate.
The positions of the satellites are determined based on a network of ground tracking stations independent of the positioning receivers. They are communicated to the positioning receivers by the satellites themselves via the data modulating the transmitted signals.
The pseudo-distances are deduced by the positioning receivers from the apparent delays exhibited by the received signals: these signals are time-stamped on transmission by the clocks of the satellites, which are synchronized on the system time, and on receipt by the clock of the receiver, possibly exhibiting a bias relative to the system time. The distances deduced from the duly measured propagation times are called pseudo-distances because they are corrupted by a common error that can be significant, due to the bias of the clock of the receiver. This bias is eliminated on resolution of the fix provided that the signals from at least four satellites are received.
While the accuracy with which the positions of the satellites of the positioning system are known is independent of the performance of a positioning receiver, such is not the case for the pseudo-distance measurements which depend on the accuracy of the signal propagation time measurements on the receiver.
The radiofrequency signals transmitted by the satellites travel over long distances and are transmitted with limited power, so they arrive with very low power at the receivers, drowned in a radiofrequency noise. To enhance their reception efforts have been made to make them as insensitive as possible to narrowband interferences, by augmenting their bandwidths using the spread bandwidth technique. The current and anticipated near-future satellite positioning systems use, for the radiofrequency signals transmitted by their satellites, the modulation bandwidth spreading technique using pseudo-random binary sequences, a technique called DSSS (Direct Sequence Spread Spectrum). This DSSS modulation consists, after having converted the data to be transmitted into the form of a series of bits at regular bit rate, in calculating the product of each information bit with a pseudo-random binary sequence known in advance with a significantly faster bit rate. The resulting spread bandwidth is proportional to the bit rate of the spreading pseudo-random bit stream. The term “spreading code” is used.
The data to be transmitted by the satellites, once formatted as a spread frequency bit stream by a spreading code according to the DSSS technique, is transposed into the transmit frequency band by modulation with a transmit carrier.
On reception, the data contained in a radiofrequency signal from a satellite of a positioning system is extracted by two successive demodulations: a first demodulation using a carrier generated locally by an oscillator driven by a frequency and phase tracking loop called PLL (Phase-Locked Loop)—or carrier phase loop—used to transpose the received signal into baseband and a second demodulation using spreading code generated locally by a code generator driven by a delay tracking loop called DLL (Delay-Locked Loop)—or code loop—used to unspread the bit stream present in the received signal. The spreading codes generated locally are identical to those transmitted by the satellite, apart from the delay due to the propagation in space.
When a code loop is locked on, the code generated locally is in phase with the code contained in the signal received from the satellite.
Thus, the delays affecting the received spreading codes can be accessed in the code loop control signals. The delays observed by these loops allow for unambiguous or almost unambiguous measurements of the propagation times of the signals because the numbers of entire pseudo-random sequences repeated elapsing during the travel of the signals are relatively small. The term “code measurements” is used.
For example, for the GPS (Global Positioning System) satellite positioning system, the shortest repeated pseudo-random binary sequence, the one used for spreading C/A (Coarse/Acquisition Code or Clear/Acquisition Code) type satellite signals, is made up of 1023 bits with a bit rate of 1.023 MHz and a duration of one millisecond. Its overall duration corresponds to a travel distance of 300 km for a radiofrequency wave and therefore allows for modulo 300 km distance measurements. The 1 microsecond duration of each of its bits provides for an accuracy of around 0.1 microseconds. The ambiguity of the pseudo-distance measurements obtained from the pseudo-random binary sequence of a C/A code due to the fact that modulo 300 km measurements are being taken is easy to eliminate when the receiver receives from more than four satellites because it can then run a coherency check and retain only the coherent solution. In the absence of such a possibility, the ambiguity can also be eliminated using a very rough prior knowledge of the position. Such a measurement ambiguity does not arise with the type P satellite signals of the GPS system which use for their spreading a non-repeated encrypted pseudo-random binary sequence, but these signals are not freely available to the users.
The apparent delays of the transmit carriers can be accessed, modulo the periods of these carriers, by the local phases produced by the PLL carrier phase loops driving the local carrier generators. The term “phase measurements” applies. These measurements are very accurate but highly ambiguous. In the case of the GPS system, the signals accessible to the public use a 1.575 GHz carrier allowing pseudo-distance measurements that are modulo 0.19 m and therefore highly ambiguous, since the distance to the satellite is around 20 000 km.
Some satellite navigation systems use pairs of carrier frequency signals that are close together so as to be able to use them coherently and thus improve the accuracy of the position measurements, due to a broader spectrum.
FIG. 1 represents the spectra of a pair of signals transmitted by a satellite. Each satellite transmits two signals a and b, each comprising a carrier modulated by a pseudo-random code which spreads the spectrum. The two signals, in this example E5a (signal a) and E5b (signal b) having carrier frequencies that are different but very close, are sent synchronously, the relations between the phases of the two carriers and of the two spreading codes in transmission being known at all times.
Hereinafter, the following notations and definitions will apply:
The central carrier frequency is, by definition, the frequency located in the middle of the two carrier frequencies (for example, E5a and E5b).
The sub-carrier frequency is, by definition, the distance between the carrier frequency of the signal a or b and the central carrier frequency (or Fb−Fp=Fp−Fa).
Notations:
Fp Central carrier frequency Fp=(Fa+Fb)/2
Fsp Sub-carrier frequency Fsp=(Fb−Fa)/2
Fa Carrier E5a frequency Fa=Fp−Fsp 
Fb Carrier E5b frequency Fb=Fp+Fsp 
Fc Code frequency
ωp=2π·Fp Central carrier pulsing ωp=(ωa+ωb)/2
ωsp=2π·Fsp Sub-carrier pulsing ωsp=(ωb−ωa)/2
ωa=2π·Fa Carrier E5a pulsing ωa=ωp−ωsp 
ωb=2π·Fb Carrier E5b pulsing ωb=ωp+ωsp 
λp=2π/Fp Central carrier wavelength
λsp=2π/Fsp Sub-carrier wavelength
λa=2π/Fa Carrier E5a wavelength
λb=2π/Fb Carrier E5b wavelength
λcode=1/Fc Code wavelength
In the rest of the document, the expression expi(θ) will be used for ejθ where j2=−1
In the case of bi-frequency services, the two signals in the receiver can be tracked independently on each band by PLL and DLL tracking loops. The pseudo-distance measurements, which rely on the delays observed by the code loops, are limited in accuracy by the width of each available band. Because of the independence of the tracking loops, any combined use of the measurements obtained from different bandwidth signals will give an accuracy limited by the less good of the two trackings.
It is, however, possible to improve the accuracy of the pseudo-distance measurements within the context of a bi-frequency service, with synchronous navigation signals, by combining the signals received on the two frequencies to benefit from a greater equivalent frequency bandwidth.
FIG. 2 shows the input analogue stages of a satellite positioning receiver using a pair of carriers E5a, E5b, as represented in FIG. 1. The analogue paths Va, Vb between the antenna and the intermediate frequency (IF) analogue/digital converters ADC 12, 14 have separate elements between the two received signals S1 and S2, which results in propagation and phase delay differentials.
FIG. 3 shows one of the two identical digital stages of a satellite positioning receiver of the state of the art driven by one of the two intermediate frequency (IF) digitized components E5a or E5b at the output of the analogue stage of FIG. 2. Each digital stage comprising a carrier correlation circuit 20 followed by a code correlation circuit 22.
For each satellite signal (E5a or E5b), a processing according to the state of the art is carried out with a carrier phase loop and a code loop. For this, a local carrier PI and local codes Ca, Cp, Cr are generated to demodulate the signal by correlation. The term “tracking channel” is used.
The phase of the local carrier PI and the position of the local codes in phase with the received signal are controlled using the tracking loops of each channel. Each tracking loop comprises, for the carrier loop, a carrier discriminator DSP, a carrier corrector CRP controlling a carrier oscillator NCOp 24 generating a carrier local phase driving a carrier generator 26 supplying the local carrier for the carrier correlation circuit and, for the code loop, a code discriminator DSC, a code corrector CRC controlling a code oscillator NCOc 28 generating a phase local code driving the code generator 30 generating the local codes Ca, Cp, Cr (advance, spot and delay) for the code correlation circuit.
The code and carrier phase discriminators make it possible to measure at the output of the correlators after integration by the integrators INT, the carrier phase and code differences between the received signal and the local signal, for retrospective action in the tracking loops.
The carrier phase loop helps the code loop driving the code local oscillator NCOc in order to reduce the loop trailing due to the dynamic range, which makes it possible to reduce the code loop band and therefore the noise on the measured code phase.
This processing is carried out in parallel for each signal from a satellite (or one channel for each satellite signal). The different, decorrelated codes from one satellite to another make it possible to dissociate the signals between the satellites and therefore allocate a channel to a satellite.
The measurements are the phases of the local carrier φpb (rad) and of the local code φcb (s) for each channel.
The role of the numerically controlled oscillators NCOp or NCOc is to produce the phases of the local high speed signals (>10 MHz) from the phase velocity controls generated by the low speed signal processing software (<1 kHz)
The role of the integrators INT is to produce the demodulated, unspread, aggregated signal samples ZA, ZP, ZR (advance, spot and delay) at low speed (<1 kHz) for the signal processing software from products output from the code demodulators generated at high speed (>10 MHz).
The “code demodulator” is the multiplier between the complex, carrier-mode demodulated received signal, and a local code. The complex resultant product is the unspread demodulated received signal.
The term “complex correlator” is used to mean the assembly comprising a code demodulator and an integrator (INT) with periodic reset (Integrate & Dump). In this case, we have three complex correlators producing ZA, ZP, AR.
The processing of the two signals S1 and S2 (for example E5a and E5b) in the input stages of the receiver in separate analogue paths introduces different propagation times and phase delays on the two carriers (subsequently called delay differentials and phase differentials) which causes the coherence between the two components to be lost and causes the accuracy of the receiver measurements to be reduced (the signals can no longer be added together constructively), and biases the measurements.